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Fibonacci Series Using Recursion
Fibonacci Series Using Recursion
Fibonacci series generates the subsequent number by adding two previous numbers. Fibonacci series starts from two numbers − F0 & F1. The initial values of F0 & F1 can be taken 0, 1 or 1, 1 respectively.Fibonacci series satisfies the following conditions −
Fn = Fn-1 + Fn-2
Hence, a Fibonacci series can look like this −
F8 = 0 1 1 2 3 5 8 13
or, this −
F8 = 1 1 2 3 5 8 13 21
For illustration purpose, Fibonacci of F8 is displayed as −
Fibonacci Iterative Algorithm
First we try to draft the iterative algorithm for Fibonacci series.
Procedure Fibonacci(n) declare f0, f1, fib, loop set f0 to 0 set f1 to 1 <b>display f0, f1</b> for loop ← 1 to n fib ← f0 + f1 f0 ← f1 f1 ← fib <b>display fib</b> end for end procedure
Fibonacci Recursive Algorithm
Let us learn how to create a recursive algorithm Fibonacci series. The base criteria of recursion.
START Procedure Fibonacci(n) declare f0, f1, fib, loop set f0 to 0 set f1 to 1 display f0, f1 for loop ← 1 to n fib ← f0 + f1 f0 ← f1 f1 ← fib display fib end for END
Example
Following are the implementations of the above approach in various programming languages −
#include <stdio.h> int fibbonacci(int n) { if(n == 0){ return 0; } else if(n == 1) { return 1; } else { return (fibbonacci(n-1) + fibbonacci(n-2)); } } int main() { int n = 5; printf("Number is: %d", n); printf("\nFibonacci series upto number %d are: ", n); for(int i = 0;i<n;i++) { printf("%d ",fibbonacci(i)); } }
Output
Number is: 5 Fibonacci series upto number 5 are: 0 1 1 2 3
// C++ Code for Fibonacci series #include <iostream> using namespace std; int fibbonacci(int n) { if(n == 0){ return 0; } else if(n == 1) { return 1; } else { return (fibbonacci(n-1) + fibbonacci(n-2)); } } int main() { int n = 5; cout<<"Number is: "<<n; cout << "\nFibbonacci series upto number "<<n<< " are: "; for(int i = 0;i<n;i++) { cout << fibbonacci(i) << " "; } }
Output
Number is: 5 Fibbonacci series upto number 5 are: 0 1 1 2 3
// Java Code for Fibonacci series public class Fibonacci { public static int fibonacci(int n) { if (n == 0) { return 0; } else if (n == 1) { return 1; } else { return fibonacci(n - 1) + fibonacci(n - 2); } } public static void main(String[] args) { int n = 5; System.out.print("Number is: " + n); System.out.print("\nFibonacci series upto number " + n + ": "); for (int i = 0; i < n; i++) { System.out.print(fibonacci(i) + " "); } } }
Output
Number is: 5 Fibonacci series upto number 5: 0 1 1 2 3
#Python code for fibonacci Series def fibonacci(n): if n == 0: return 0 elif n == 1: return 1 else: return fibonacci(n-1) + fibonacci(n-2) if __name__ == "__main__": n = 5 print("Number is ", n) print("Fibonacci series upto number ",n, "are: ") for i in range(n): print(fibonacci(i) , end = " ")
Output
Number is 5 Fibonacci series upto number 5 are: 0 1 1 2 3
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